Can I use cycles renderer for a game?
Yes and no:

see this for "what is baking"

and this for "how to bake in cycles"

I say "yes and no" because no, you cannot use a complicated raytracing render engine realtime in a game (unless you have like, some sort of super computer :D)
But yes cycles can improve your games visuals and even make them appear like they were rendered in cycles if you do it right.

Also yes the light will look "glued" to the object, but no, with specular maps and only baking a diffuse pass it does not have to be, and can be 100% dynamic.

Since I know next to nothing about Unity (game engine or otherwise), we will discuss this in terms of blender.

First of all, you want to only bake certain passes for a game texture.

I only use "Diffuse Direct" and "Ambient Occlusion"
you can change the pass in the little box "Bake type"


This will ensure that no reflections/lights will be baked into your object, especially if you only use Ambient occlusion

If you want to get really fancy, you can bake out or paint a specular map, which will make your object only reflective on certain parts, and usually makes games look better. :D